Noncommutative space-time models

Abstract

The FRT quantum Euclidean spaces O N q are formulated in terms of Cartesian generators. The quantum analogs of N-dimensional Cayley-Klein spaces are obtained by contractions and analytical continuations. Noncommutative constant-curvature spaces are introduced as spheres in the quantum Cayley-Klein spaces. For N = 5 part of them is interpreted as the noncommutative analogs of (1+3) space-time models. As a result the quantum (anti) de Sitter, Minkowski, Newton, Galilei kinematics with the fundamental length and the fundamental time are suggested.